c International Institute for Applied Systems Analysis 22€¦ · Sabelis MW, van Baalen M, Pels B, Egas M & Janssen A (2002). Evolution of Exploitation and Defense in Tritrophic

Sabelis MW, van Baalen M, Pels B, Egas M & Janssen A (2002). Evolution of Exploitation and Defense inTritrophic Interactions. In: Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management,

eds. Dieckmann U, Metz JAJ, Sabelis MW & Sigmund K, pp. 297–321. Cambridge University Press.c© International Institute for Applied Systems Analysis

22Evolution of Exploitation and Defense in Tritrophic

InteractionsMaurice W. Sabelis, Minus van Baalen, Bas Pels, Martijn Egas,

and Arne Janssen

22.1 IntroductionWhy do plants cover the earth and give the world a green appearance? This ques-tion is not as trivial as it might seem at first sight. Hairston et al. (1960) hypothe-sized that herbivores cannot ransack the earth of its green blanket because they arekept low in number by predators. They tacitly ignored the possibility that plantsdefend themselves directly against a suite of herbivores and together exhibit suchgreat diversity in defense mechanisms that “super” herbivores able to master allplant defenses did not evolve and those that overcome the defenses of some plantsare limited by the availability of these plants. Strong et al. (1984) recognized bothpossibilities in their review on the impact of herbivorous arthropods on plants, butthey also favored the view that predators suppress the densities of herbivores, andthereby reduce the threat of plants being eaten.

The two explanatory mechanisms (plant defense versus predator impact), how-ever, may well act in concert. Ever since the seminal review paper by Priceet al. (1980) ecologists have become increasingly aware that plant defenses in-clude more than just trickery to reduce the herbivore’s capacity for (population)growth. For example, the plant may provide facilities to promote the foraging suc-cess of the herbivore’s enemies. This form of defense is termed indirect as opposedto direct defense against herbivores. Examples of direct defenses are:

� Plant structures that hinder (feeding by) the herbivore (e.g., cuticle thickness,“smooth” cuticle surfaces that do not provide a holdfast, impenetrable massesof leaf trichomes, glandular trichomes acting as sticky traps);

� Secondary plant compounds that modify the quality of ingested plant food (di-gestion inhibitors), intoxicate the herbivore, or signal the plant’s well-defendedstate to “discourage” the herbivore (feeding deterrents).

Indirect plant defenses bypass the direct defense route against the second trophiclevel by promoting the effectiveness of the third. For example, plants may retainthe herbivore’s enemies by providing protection and/or food and they may attractthese enemies by betraying the presence of prey via herbivory-induced chemicalplant signals. When Price et al. (1980) published their review paper, certain ant–plant interactions provided the best-known examples of indirect defenses [Janzen

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298 E · Multilevel Selection

1966; Bentley 1977; see also reviews by Beattie (1985) and Jolivet (1996)]. Now,more than 20 years later, it has become increasingly clear that the conspiracy be-tween plants and predators against herbivores is a widespread phenomenon; a widerange of plants from many different families invest in promoting the effectivenessof a suite of predatory arthropods (Beattie 1985; Buckley 1986, 1987; Dicke andSabelis 1988, 1989, 1992; Dicke et al. 1990; Koptur 1992; Drukker et al. 1995;Takabayashi and Dicke 1996; Turlings et al. 1995; Jolivet 1996; Walter 1996;Scutareanu et al. 1997; Sabelis et al. 1999a, 1999b, 1999c, 1999d).

In this chapter, we outline how analysis of the way plants defend themselvesagainst herbivores can shed light on certain issues in host–parasite interactions.Many analogies exist between plant–herbivore interactions and host–parasite in-teractions. In fact, arthropod herbivores can easily be considered as “parasites”of the plants: compared to their host they are small, and the detrimental effectsincurred result not so much from the effect of a single herbivore, but rather fromthe combined effects of the population that develops. Thus, it is in the interest ofthe plant to slow local herbivore dynamics as much as it is in the interest of ananimal host to block within-host parasite dynamics. As argued above, plants maydo so by direct means of defense, but they may also solicit the help of the predatorsof the herbivores. Thus, predators may function effectively as a kind of “immunesystem” for the plants. Insights into plant–herbivore–predator interactions maytherefore provide clues to understand evolutionary aspects of host–parasite inter-actions. Our approach, as it is explicitly based on models for local populationinteractions between herbivore and predator, can be used to assess how, by chang-ing certain parameters, the plant can manipulate the interaction to its own benefit.We use this approach not only to expose the game-theoretic aspects of the inter-action between trophic levels, but also the interactions within these levels. Localcompetition among predators or herbivores has a clear link with the evolution ofvirulence, as this can also be strongly affected by within-host competition (Nowakand May 1994; Van Baalen and Sabelis 1995a).

We treat the system as a simple linear food chain of plants, herbivores, andpredators, and hence ignore the many and varied ways of “cheating and misusing”that exist in complex food webs of arthropods on plants. We prefer to concen-trate here on the evolution of food exploitation strategies of the herbivores andpredators in response to investments in direct and/or indirect defenses on the partof the plant. Typically, herbivorous arthropods may (evolve to) be mild or malig-nant parasites of the plant and predatory arthropods may (evolve to) be prudent orwasteful exploiters of the population of herbivorous arthropods on a plant. Clearly,for a plant to invest in direct and/or indirect defense, it matters how virulent theherbivorous arthropods are to the plant and how virulent the predatory arthropodsare to the population of herbivores on a plant. We argue that, to understand theevolution of mutualistic interactions between plants and the natural enemies ofherbivorous arthropods, we should identify the advantages to the individual plantand the individual predator, predict the consequences for the population dynam-ics of herbivorous and predatory arthropods, and elucidate how dynamics in turn

22 · Evolution of Exploitation and Defense in Tritrophic Interactions 299

affects the evolution of plant–predator mutualism and the herbivore’s response tothis conspiracy. Whereas a definitive solution is not within reach, we hope to con-vince the reader that there are many possible outcomes for the evolution of defenseand virulence in this tritrophic system, and we discuss the consequences of theseinsights for the “world is green” hypothesis and the common notion that plant–predator mutualisms readily evolve because “it is both in the interest of plants toget rid of the herbivores and in the interest of the predators to find herbivores asprey” (Price et al. 1980).

First, we briefly discuss that the players in the tritrophic game operate on verydifferent spatial and temporal scales. Second, we introduce a simple model oflocal predator–prey dynamics on an individual plant based on specific scale as-sumptions and use this model to identify the main categories of defensive strate-gies of a plant, as well as the main strategies of food exploitation by the herbivoresand the predators. Third, we identify evolutionarily stable strategies (ESSs) of ex-ploitation (predator–herbivore, herbivore–plant), migration (predator, herbivore),and defense (plant, herbivore) in tritrophic systems. Finally, we speculate on theconsequences for virulence management.

22.2 Spatial and Temporal Scales of InteractionPlants, herbivorous, and predatory arthropods are engaged in interactions withwidely different temporal scales. Plants usually have much longer generation timesthan arthropods. Hence, plant population change tends to be slow relative to thatof the arthropods. Hence models of arthropod predator–prey dynamics are usuallydecoupled from plant population dynamics by assuming a pseudo-steady state.The generation times of herbivorous and predatory arthropods may also differ, butare usually close enough to justify modeling as a ditrophic system (Hassell 1978;Sabelis 1992).

The spatial scale of predator–prey interaction is set by the distribution of her-bivorous arthropods. Many herbivorous arthropods have strongly clumped distri-butions over their host plants. This may be the result of:

� Aggregation toward weakened host plants or hosts whose defenses are over-whelmed by pioneer attacks, as in bark beetles (Berryman et al. 1985; de Jongand Sabelis 1988, 1989);

� Large egg clutches deposited by a female, as in various species of moths (larchbud moths, gypsy moths, ermine moths, tent caterpillars, and brown tail moths);

� Multigeneration congregations that result from one or a few founders with ahigh intrinsic capacity of population increase (relative to the rate of emigra-tion) and low per capita food demands, as in many small herbivorous arthro-pods with short generation times (scale insects, mealybugs, aphids, leafhoppers,whiteflies, thrips, spider mites, and rust mites).

These groups of herbivorous arthropods may occupy a leaf area less than that of aplant, or cover several neighboring plants. Moreover, group size and the leaf areaoccupied increase with the number of generations spent in the group and with the


extent to which the herbivores move to neighboring host plants instead of dispers-ing far away. These traits are of crucial importance to understand plant defenses,because individual plants (or kin groups of plants) are the units of selection and theselective advantage of defense depends on the extent to which a plant can influencethe local dynamics of herbivores and predators by direct and/or indirect defenses.Indeed, this influence is limited because predators and herbivores are independentplayers in the game: they may decide to stay, to move to neighboring plants, or todisperse far away. Hence the question is: does the defense of an individual plantinitially affect the herbivore population it harbors (and much later the herbivorepopulation as a whole) or does its impact on the herbivores permeate population-wide and without delay (as a consequence of high herbivore mobility)? Much thesame questions can be formulated with respect to the degree in which individualplants can monopolize the advantages from attracting natural enemies of the her-bivores. To analyze the complexities that arise from spatial and temporal scaleswe start by assuming that plants investing in direct and indirect defense acquire allthe benefits, and later we consider the case in which neighboring plants may profittoo.

22.3 Predator–Herbivore Dynamics on Individual PlantsTo understand the range of possible plant defense strategies it is instructive tomodel the dynamics of small arthropod herbivores at the scale of an individualplant (or a coherent group of clonal plants). For reasons of simplicity we assumethat the spatial scale covered by a local predator and prey population is smaller thanthat of an individual plant (or group of ramets) and that the individual plant doesnot impose a carrying capacity on the arthropod population that inhabits the plant.Moreover, we limit our discussion to the case of local populations with multipleand overlapping generations, as is realistic for small arthropods. Our aim is tofind the simplest possible model for the dynamics of herbivorous and predatoryarthropods and then ask the question how an individual plant can reduce damageby influencing the herbivores and their predators.

We assume that prey form patchy aggregations, which consist of clusters ofherbivore-colonized leaves, and that predators entering such patches can freelymove around, and spend little time in moving between herbivore-colonized leavesrelative to the time spent within the herbivore colonies. Moreover, predators tendto avoid each other (Janssen et al. 1997a) and thereby interference (Nagelkerke andSabelis 1998). Thus, the cluster of herbivore-colonized leaves can be considered asa coherent and homogeneous arena for strongly coupled predator–prey interactions(Figure 22.1). The population of herbivores in such a cluster presents to a predatorin the same way as a host does to a pathogen. In fact, local predator–prey dynamicsare much more transparent, and have been much more thoroughly studied, thanwithin-host parasite dynamics. Usually, the latter are treated as a black box [butsee Box 12.1 and, in addition, Nowak et al. (1991), Sasaki and Iwasa (1991),Antia and Koella (1994), for models that take within-host dynamics explicitly into


Leaf

Plants

Cluster ofcolonies

Patch

Figure 22.1 A patchy infestation of small herbivorous arthropods in a row of plants (side-view). It is inspired by observations on spider mites, but in essence applies to many otherherbivorous arthropods. The infested leaf parts are excised (middle) and then put togetheras a jigsaw puzzle (bottom). The latter forms the patch or arena within which the interactionbetween predator and prey takes place (assuming negligible time spent in moving betweeninfested leaves).

account], whereas various simple models capture the essence of local predator–prey dynamics.

To derive one example of such a model, we assume that the predators search forthe highest prey densities and minimize interference with (intraspecific) competi-tors. In addition, we assume that within newly (and expanding) infested leaf areasherbivore density is typically constant, a characteristic determined by the herbi-vore or the combination of herbivore and plant (Sabelis 1990; Sabelis and Janssen1994). Thus, per unit of plant area, herbivores raise a fixed amount of offspringand predators reaching a freshly colonized leaf site continue to eat prey until theydo better by moving to a site nearby on the same plant. These assumptions leadto a constant rate of predation, which is much like “eating a pancake”: a constantamount of food at each bite until there is nothing left.

As long as the pancake is not completely eaten, predators maximize the percapita rate of predation, development, and reproduction. Hence, under conditionsof a stable age distribution they achieve their intrinsic rate of population increase.Similar assumptions are made with respect to herbivore growth capacity in theabsence of the predators. For the case in which predators stay until all the preyare eaten, the dynamics of predator and herbivore numbers can be described bythe two linear differential Equations (22.1a) and (22.1b). These differ from theclassic Lotka–Volterra models in that the predation term now only depends on thenumber of predators (Metz and Diekmann 1986, example III.1.10; Janssen and


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Figure 22.2 Three types of local predator–prey dynamics (continuous curve for predatorsand dashed curve for prey) according to the pancake predation model [with parametersrN = 0.3, k = 1, rP = 0.25, m P = 0, and N (0) = 25]. (a) Prey increase, P(0) = 1, (b)delayed prey decline, P(0) = 3, and (c) immediate prey decline, P(0) = 8. The generalconditions for each of these types of dynamics are discussed in the text.

Sabelis 1992; Sabelis 1992),

d N

dt= rN N − k P , (22.1a)

d P

dt= rP P . (22.1b)

This is the so-called “pancake predation” model with t = the time since start ofthe predator–prey interaction, N (t) = number of prey at time t , P(t) = number ofpredators at time t , rN = rate of prey population growth, k = maximum predationrate, and rP = rate of predator population growth. Analytical solutions for thenumber of predators and prey since the start of the interaction are readily obtained,

N (t) = N (0)erN t − P(0)k

rP − rN(erP t − erN t ) , (22.2a)

P(t) = P(0)erP t . (22.2b)

Three types of dynamical behavior of the prey population may occur:

� Continuous increase (but at a pace slower than the intrinsic rate of prey popula-tion growth; Figure 22.2a);

� Initial increase, followed by decrease until extinction (Figure 22.2b);� Continuous decay until extinction (Figure 22.2c).

In the first case only, predatory arthropods cannot suppress local prey populationoutbreaks, but in the two other cases they eliminate the prey population and growexponentially until a time τ when all the prey are eaten and all the predators em-igrate. This time τ from predator invasion to prey extinction can be expressed as


a function of rN , k and rP and the initial numbers of predator and prey, N (0) andP(0),

τ = 1

rP − rNln

[1 + rP − rN

k

N (0)

P(0)

]. (22.3)

Immediate decline of the herbivores occurs when the net growth rate of the herbi-vore population is negative, rN N (0) < k P(0), or

P(0)

N (0)>

rN

k. (22.4a)

Thus, for the herbivore population to decline immediately, the ratio of predators toherbivores should exceed the ratio of the per capita population growth rate of theherbivore and the maximum per capita predation rate.

The conditions for continued herbivore increase are found by calculating thecondition for which the time to prey extinction has a finite value. Provided that theplant is not overexploited during predator–prey interaction, this condition is

P(0)

N (0)≤ rN − rP

k. (22.4b)

This condition cannot hold when the growth rate of the prey does not exceed thatof the predator, rN ≤ rP . Whenever the condition is met, however, herbivorescontinue to increase and predators “surf” on the “population growth wave” of theherbivore. Inevitably, this increase stops when the plant becomes overexploited.

The total damage incurred by the plant over the whole interaction period can beexpressed in the number of herbivore-days D, that is, the area under the curve thatexpresses the temporal changes in the size of the herbivore population,

D(τ, rN , k, rP , N (0), P(0)) = 1

rN

[P(0)

k

rP(erPτ − 1) − N (0)

]. (22.5)

Note that this measure of the damage strongly depends on the exponential term andthus on the time to prey extinction τ and the per capita growth rate of the predatorpopulation rP .

Thus, given the initial population sizes N (0) and P(0) and estimates of theparameters rN , k, rP , it is possible to assess the overall damage by the herbivoreand the predator’s potential to suppress the prey population immediately, with adelay, or not at all. Now, we may ask how a plant can influence the local dynamicsso as to minimize herbivore damage. Under the assumption that the parameterscan be modified independently, the answer is straightforward. It should:

� Make the predator-to-herbivore ratio as high as possible;� Increase the predation rate or the predator growth rate;� Decrease the growth rate of the herbivore.

To illustrate this, the plant may attract and retain the predators by providing SOSsignals upon herbivore attack, it may provide food and shelter for the predators,and produce toxins or digestion inhibitors.


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Figure 22.3 Dynamics of predatory mites (Phytoseiulus persimilis Athias-Henriot; contin-uous curves) and herbivorous mites (Tetranychus urticae Koch; dashed curves) at variousspatial scales. (a) Circular system of eight interconnected islands (trays), each with 10Lima-bean plants maintained in the two-leaf stage (by frequent removal of the apex andreplacement of plants exhausted as a food source). Source: Janssen et al. (1997b). (b)Extinction-prone predator–prey dynamics on one super-island (the size of eight trays to-gether). (c) Two replicate experiments showing persistent predator–prey metapopulationdynamics on the eight-island system in (a). (d) Extinction-prone predator–prey dynamicson one of the trays shown in (a). Source: Janssen et al. (1997b); see also Van de Klashorstet al. (1992). (e, left) Extinction-prone predator–prey dynamics on a single leaf in a windtunnel, using a field-collected predator line selected for nondispersal before prey extermina-tion. Source: Pels and Sabelis (1999); see also Sabelis and Van der Meer (1986). (e, right)As (e, left), but now using a field-collected predator line selected for dispersal before preyextermination. Source: Pels and Sabelis (1999).

Trade-off relations between parameters may complicate matters. For exam-ple, decreasing the growth rate of the herbivore rN by toxins may also intoxicatethe predator, thereby decreasing the predation rate k and/or its growth rate rP .In the extreme, the herbivore may even use the plant-provided toxins to defenditself against predators. Thus, the plant does not always profit from decreasingthe growth rate of the herbivore. It only profits if it decreases the herbivore’sgrowth rate proportionally stronger than the predation rate and the growth rate ofthe predator.

Another message gleaned from the equations is that plants may benefit frompromoting the presence of predators with high predation rates and high growthrates. Often, these demands are in conflict with each other, because the predationrate tends to increase with body size, whereas the intrinsic rate of population in-crease tends to decrease with body size (Sabelis 1992). Such relationships withbody size are clear from analyzing published data on predators of phytophagousthrips, such as mirids, anthocorids, predatory thrips, and predatory mites (Sabelisand Van Rijn 1997). At lower taxonomic levels (within family, within genus)the picture may be different. For example, within the Phytoseiidae – a family ofplant-inhabiting predatory mites – positive high correlations between k and rP ex-ist (Janssen and Sabelis 1992; Sabelis and Janssen 1994). It may be possible thatthe plant could selectively attract one species of predator over the other and therebyprofit from selecting the more effective predators. However, how a plant could doso, given that predators will seek the most profitable prey, remains to be shown.

Predators are independent players in the tritrophic game and they decidewhether it is profitable to stay on a plant or not. The pancake predation model isbased on the assumption that predators are strongly retained and stay until all theprey are eaten. This scenario is not implausible, because it may be risky to disperseand search for new herbivore patches. Indeed, it is frequently observed, as in in-teractions among predatory mites and spider mites (Figure 22.3a; Sabelis and Vander Meer 1986). One may, of course, expect predators to leave somewhat earlierthan the exact moment of prey extinction. This would relieve the herbivores from


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Figure 22.4 Influence of emigration on local predator–prey dynamics according to thepancake model. (a) Predator emigration rate m P equals zero for predator and prey curvesindicated by filled arrowheads, whereas it is 0.04 for the predator and prey curves indicatedby open arrowheads. Parameters: m P = 0 or 0.04, rN = 0.3, k = 3, rP = 0.25, N (0) =30, P(0) = 1. (b) Prey emigration rate m N equals zero for dashed predator and prey curves(open arrowheads) and 0.1 for the continuous predator and prey curves (filled arrowheads).Parameters: m N = 0 or 0.1, rN = 1, k = 1, rP = 1.5, N (0) = 50, P(0) = 1.

predation pressure and predator-to-prey ratios may become so low that the herbi-vore population increases again, thereby giving rise to cyclic dynamics. The plantwould then accumulate damage over the predator–prey cycles whereas it would bebetter off when predators exterminate the herbivores or maintain them at a verylow level. Examples of local predator–prey dynamics are shown in Figure 22.3for interactions between phytoseiid predators and spider mites. Similar examplesare known from interactions between phytoseiid mites and thrips, and anthocoridpredators and thrips (Sabelis and Van Rijn 1997). All these examples convincinglyshow that local herbivore populations are strongly suppressed by predators. Thus,the dynamics of the “pancake predator” model seems to be a good caricature ofthe initial predator–prey population cycle. Thus, for all cases in which one cycleof predator and prey colonization occurs before extermination, this model is usefulto understand the role of indirect and direct defenses of a plant.

Predator retention during the interaction with the herbivores is decisive in thesuccess of indirect defense strategies of the plant. For example, if we extend thepancake predator model with a constant predator emigration rate (i.e., indepen-dent of prey availability), then emigration acts to decrease the effective populationgrowth rate of the predators. As shown in Figure 22.4a small decreases of the pop-ulation growth rate have dramatic consequences for the duration of the interactionand even more for the number of herbivores attacking the plant. The overall dam-age to the plant increases nonlinearly with a reduction of the predator’s populationgrowth rate. Hence, it is important to observe that several species of predatorsare strongly retained in herbivore-colonized patches and tend not to leave until theprey population is near extinction (Sabelis and Van der Meer 1986; Sabelis andVan Rijn 1997; Pels and Sabelis 1999; Figure 22.3e).


The herbivore can always make the last move in the tritrophic game. Not onlymay they develop resistance against the predators and overcome barriers raisedby the plant, but ultimately, they may also decide to leave the plant. If the plantdrives herbivores away by attracting predators, and also by stimulating herbivoreemigration, then it benefits disproportionately, as illustrated in Figure 22.4b.

In conclusion, there are various ways in which a plant can benefit by influencingbehavior and dynamics of predators and herbivores. Direct plant defenses do notmerely slow down the herbivore’s growth rate, they may also affect predator im-pact, either positively (higher predator-to-herbivore ratio) or negatively (plant tox-ins protecting herbivores against predators). Indirect defenses do not merely affectpredator performance, they may also affect selection on herbivores, be it positive(enemy avoidance) or negative (resistance to predators) for the plant. Hence, to un-derstand the plant’s allocation to direct and indirect defenses we should not onlyassess the costs, but also elucidate how these two types of defenses interact in theirimpact on overall herbivore damage.

22.4 Tritrophic Game Theory and Metapopulation DynamicsThe evolution of direct and indirect plant defenses against arthropod herbivoresis by no means a simple process. For one thing, we have to take the defenseand exploitation strategies of all three trophic levels into account. For another,time scale and spatial scale arguments force us to consider metapopulation modelswith the full tritrophic structure, and – as we emphasize later – to incorporate plantdynamics adds new dynamical behavior to the repertoire of the otherwise ditrophicmodels.

Indeed, evolution in structured populations can only be properly understoodby taking metapopulation structure into account. The strategies play against eachother at the patch level and their relative success determines metapopulation dy-namics. In turn, metapopulation processes determine which strategies will meetand compete again at the patch level. This chain of processes is referred to hereinas the ecological feedback.

To gain insight into this complex problem, carefully planned simplificationsare required. Our strategy is first to consider the evolution of relevant traits atone trophic level in pairwise interactions with one other level (predator–herbivore;herbivore–predator; plant–herbivore; herbivore–plant; plant–predator; predator–plant), thereby assuming a steady state at the metapopulation level. We concludewith a tentative, verbal discussion of what may happen evolutionarily in the fulltritrophic system.

The predator’s dilemma: to milk or to kill?It is one thing for a plant to attract and retain predators, but it is another to lurepredators that also effectively suppress the herbivore population on the plant.Clearly, it is the predator who reacts to the lure, and decides how fast it willconsume herbivores, how fast it will multiply, and how long it will stay. In


other words, the effectiveness of indirect plant defenses depends on the herbivore-exploitation strategies present in the predator population. In principle, these ex-ploitation strategies can be many and varied. To illustrate this point it is instructiveto use the “pancake” model to examine local predator–herbivore dynamics. Thestrategy set is determined by combinations of the per capita growth rate of thepredator rP and the per capita predation rate k. However, a spatially structuredenvironment has one more parameter: the per capita emigration rate of the preda-tor. Of course, all predators disperse away when herbivores are exterminated andthere is no other food, but they can also decide to move away during the inter-action. Such increased emigration of the predator relieves the prey of predationpressure and thereby the prey population represents a larger future food source forthe predator (Van Baalen and Sabelis 1995c). This effect can also be achievedby decreased predation (Gilpin 1975). However, increased emigration during theinteraction seems a more sensible strategy, because it does not affect the intrinsicpopulation growth rate, whereas decreased predation implies lower food intake andthereby a lower population growth rate. Moreover, the extra dispersing propagulesgenerated under the former strategy will promote the founding of new populations.In what follows we therefore focus on the predator’s migration trait alone.

Let us assume for simplicity that the per capita emigration rate is a constantm P . The effective per capita population growth rate of the predators is reduced bym P so that the effective predator growth rate now equals

d P

dt= (rP − m P)P . (22.6)

As decreased values of rP have been shown to drastically alter local predator–preydynamics, so do increased values of m P . As illustrated in Figure 22.4a, a smallincrease of m P from 0 to 0.04 day−1 greatly alters the area under the prey curveand thereby also the damage to the plant. Hence, a plant benefits from stimulatingpredators to stay until all the prey are eliminated, but whether it succeeds dependson what is best for the predators (as well as on the ecological feedback). The lo-cal success of a predator’s exploitation strategy may be expressed as the numberof dispersers produced during the interaction with prey, plus those that disperseafter prey extermination. As shown in Figure 22.5, the production of dispersers in-creases disproportionally with m P and reaches an asymptote when the per capitaemigration rate is so high that the predators cannot suppress the growth of the preypopulation any more, that is, when m P = rP −rN +k P(0)/N (0). Thus, predatorsthat suppress emigration during the interaction reach their full capacity to sup-press the local prey population, but they produce the lowest number of dispersersper prey patch. In terms of production of dispersers this so-called killer strategydoes less well than the strategy of a milker, which typically has a nonvanishingemigration rate during the predator–prey interaction period. However, if killersenter a prey patch with milkers, then they would steal much of the prey the milkershad set aside for future use. Therefore, if there is a risk of invasions by killers, itpays to anticipate such events and selection will favor exploitation strategies thatare less milker-type and more killer-type.


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Figure 22.5 The relation between the overall production of predator dispersers and theper capita rate of emigration m P during the predator–prey interaction period (from predatorinvasion to prey elimination. Source: Van Baalen and Sabelis (1995c).

The outcome of the milker–killer dilemma is determined by a complex interplayof local competition between the exploitation strategies and global (= metapopula-tion) dynamics. It depends on the probability of multiple predator invasions in thesame prey patches (or, alternatively, on the probability of exploiting a prey patchalone), on the resultant production of dispersers per prey patch, and on metapop-ulation dynamics, as this in turn determines the probability of multiple invasions.The complexity of this ecological feedback is staggering; to keep track of thenumbers of each strategy type when competing in local populations, dispersinginto the global population, and invading into local populations requires a massivebookkeeping procedure. Hence, we are bound to simplify to obtain some insight.For example, Van Baalen and Sabelis (1995c) assumed that all patches start withexactly the same number of predators and prey (which assumes metapopulation-wide equilibrium and ignores stochastic variation in the number of colonizers) andthat the predators have enough time to reach their full production potential perprey patch (the assumption of sequential interaction rounds). In this setting theyconsidered the reproduction success of one mutant predator clone with a per capitaemigration rate, m P,mut, relative to the mean success of predators in the populationof the resident clone, which possesses another per capita rate of emigration, m P,res.The question is whether there exists an ESS value of m P,res for which it does notpay any mutant to deviate (Maynard Smith 1982). In particular, Van Baalen andSabelis (1995c) calculated the combinations of parameters P(0), N (0), rN , k, andrP for which it does not pay to increase m P away from zero, that is, the conditionsthat favor selection for killers. As illustrated in Figure 22.6, the general outcomeis that killers are usually favored by selection, except when the number of predatorfoundresses is low and the number of prey foundresses is high. In other words,the milkers are favored as long as they have a sufficiently large share in the localpopulations to maintain control over the time to prey elimination τ .

This analysis whets the appetite for more elaborate considerations that accountfor:


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al n

umbe

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Figure 22.6 When does it pay to increase the per capita emigration rate of the predator m Paway from zero? This diagram shows that milker strategies are only advantageous whenP(0) is low and N (0) sufficiently high. Source: Van Baalen and Sabelis (1995c).

� Asynchrony in local dynamics;� Stochastic variation in predator and prey colonization rates (since these are

probably low);� An upper boundary to prey population size set by the local amount of food;� Metapopulation dynamics.

Such extensions are likely to show that milkers which achieve a longer interactionperiod are also exposed for a longer period to subsequent predator invasions (andthus face competition with killers sooner or later), that stochastic rather than uni-form invasions help to isolate milkers, which thereby gain full advantage of theirexploitation strategy, and that limits to the amount of food available for the preydecrease opportunities for a milker, as it loses full control over the interaction pe-riod τ . As these factors have opposite effects it is not immediately clear whetherkillers or milkers will win the battle or whether they may even coexist. Computersimulations of the metapopulation dynamics of milkers and killers using a modelparameterized for phytoseiid mites (predators) and spider mites (prey; Pels et al.,in press) showed that the full ecological feedback gives rise to prey and predatordensities in which multiple predator invasions are sufficiently rare to make “milk-ers” the more successful strategy. The results of a large number of computer ex-periments to determine the average number of dispersers born from mutants withdifferent emigration strategies released randomly in the metapopulation of the res-idents (but after 2 000 days to avoid the initial phase of transient metapopulationdynamics) is summarized in the pairwise invasibility plot shown in Figure 22.7.This shows that metapopulation dynamics can force the predator–prey system intoa state [i.e., number of predator and prey colonizing a patch, N (0) and P(0), inFigure 22.6] in which “milkers” are the winners of the competition.

Apart from the need for more theoretical work, experimental analysis of varia-tion in the exploitation strategies of predators seems a promising avenue for futureresearch. Such an analysis, carried out for the predatory mite Phytoseiulus persim-ilis Athias-Henriot, revealed that laboratory cultures harbor exclusively predators


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Figure 22.7 A pairwise invasibility plot for mutants that differ from the resident preda-tors with respect to the emigration rate m P . The resident’s emigration rate is given on thehorizontal axis and the mutant’s emigration rate on the vertical axis. Gray areas indicatecombinations in which the mutant invades the resident population (the shape of the gray ar-eas is based on the simulation results indicated by crosses). The results shown are obtainedfor a value of the predator’s survival rate that allows the predator–prey system to persist.

of the killer type (Sabelis and Van der Meer 1986), whereas field-collected popu-lations in the Mediterranean (Sicily) exhibit some variation in the onset of emigra-tion before or after prey elimination (Pels and Sabelis 1999). Interestingly, mostpopulations collected along the coast, where predators are more abundant, initi-ated emigration only after elimination of the prey, whereas those collected inland,where local predator populations are scarce and hence more isolated, showed someemigration before prey elimination! These results are in qualitative agreement withthe analytic ESS analysis of Van Baalen and Sabelis (1995c; Figure 22.6), but theyseem to contradict the results of the more “realistic” computer simulations that arenot only parameterized for this particular mite system but also take into accountstochastic colonization and the full ecological feedback (Pels et al., in press; Fig-ure 22.7). This discrepancy probably results from a variety of factors that causethe predators to loose control over the exploitation of the local prey population.Examples are environmental disasters (heavy rain, wind, or fire), overexploitationof plants by large herbivores, and also exploitation competition with other preda-tor species or herbivore diseases. The discrepancy between the simulations (Pelset al., in press; Figure 22.7) and the analytic treatment (Van Baalen and Sabelis1995c; Figure 22.6) may emerge because:

� The simulations were obviously only carried out for persisting resident popula-tions, whereas the analytic treatment implicitly assumed equilibrium (and thuspersistence);

� The simulated predator–prey feedback causes patches to be invaded by verylow numbers of predators, whereas the analytic treatment presupposed a certaininvasion scenario (equal for all patches);

� The stochastic colonization process of the predators allows some patches to beinvaded singly and gives the single invader full control over the exploitation


of the local prey population, whereas the analytic treatment ignored stochasticvariation in the number of colonizers.

Obviously, the prevalence of killers is of great importance for the evolution of indi-rect plant defenses. By providing protection and food to predatory arthropods andby signaling herbivore attack to predators, plants increase the predator invasionrate into young colonies of the herbivorous arthropods. This promotes the prob-ability of coinvasions of milkers and killers, which – other things being equal –ultimately favors the latter. Yet, there may be a pitfall in that, so far, neither theo-retical nor experimental analyses addressed the possibility of more flexible strate-gies, such as: “milk when exploiting the prey patch alone, and kill when other(e.g., nonkin) predators have entered the same patch.”

In summary, how “virulent” predators should be (as “parasites” of local herbi-vore populations) depends on whether they are able to monopolize this resource.Sharing of the resource with other clones (“multiple infection”) favors increasedvirulence. How often such sharing occurs depends on the ecological feedbackloop. To a certain extent, this conclusion is more robust than those based on othermodels published in the epidemiological framework (e.g., Nowak and May 1994;Van Baalen and Sabelis 1995a), because it is based on an explicit consideration ofhow the predator’s exploitation strategies affect the interaction time in the patch(and not on some a priori assumption about the relation between parasite trans-mission and host mortality).

The herbivore’s dilemma: to stay or to leave?Just like the predators, the herbivores are independent players in the tritrophicgame. When their local populations are discovered and invaded by predators ofthe milker type, possibilities to achieve reproduction success remain, especially ifthe milker has such a high emigration rate that it cannot suppress the herbivorepopulation. However, when killers enter the herbivore population, it may pay theherbivores to invest in defense against the killer-like predators or to leave the preypatch in search for enemy-free space. For simplicity, we consider the last typeof response only. Consider the pancake predation model again, but now extendedwith a per capita emigration rate m N of the herbivore:

d N

dt= (rN − m N )N − k P , (22.7a)

d P

dt= rP P . (22.7b)

As shown in Figure 22.4b, an increase in m N causes the time to prey eliminationto decrease, as will the overall, local herbivore population (i.e., the area underthe herbivore population curve) and the number of predators that will disperse.We may now ask whether there is an evolutionarily stable (ES) emigration rate.To obtain an answer we should first define reproduction success as the per capitaemigration rate m N multiplied by the area A under the herbivore curve (which


itself depends on m N ), divided by the initial number of herbivores N (0). Thisfitness measure always shows a maximum for intermediate values of m N , becauseA decreases rapidly with m N . Suppose, for simplicity, that all patches start syn-chronously with the same initial number of predators and herbivores and that eachpatch is colonized by N (0) herbivore clones with m N ,res and just one herbivoremutant clone with m N ,mut. Further, assume that the two types of herbivore clonesare attacked in proportion to their relative abundance, but that the mutant is sorare that Nres + Nmut ≈ Nres. This makes herbivore dynamics in the patch andtime to prey elimination τ entirely dependent on the resident population. The mu-tant’s presence does not influence the growth of the resident herbivore populationand neither does it affect the growth of the predators. Herbivore dynamics in thepatch and time to prey elimination τ are thus entirely dependent on the traits ofthe resident prey population. Now, we ask whether there is a resident herbivorepopulation with m N ,res that cannot be invaded by a mutant with another value ofm N ,mut. The results presented in Figure 22.8 (Egas et al., unpublished; for modeldetails see Appendix 22.A) show that the ES emigration rate m∗

N increases with:

� Decreasing per capita population growth rate of the herbivores rN ;� Increasing per capita predation rate k;� Increasing per capita population growth rate of the predators rP , and, thus, with

a decrease in time to prey elimination τ .

Moreover, the larger the initial number of herbivores, the longer the time to preyelimination and the smaller the ES emigration rate m∗

N .These results provide some important clues as to how the ES emigration rate

m∗N will change with the exploitation strategy of the predators. This is because

predator emigration affects the effective predator growth rate as experienced bythe prey. Milkers are predators with an effectively lower per capita rate of popu-lation growth, rP − m P , because of nonvanishing emigration, and the lower thepredator’s population growth rate, the lower the ES emigration rate m∗

N of the her-bivore will be. Thus, a prevalence of milkers in the predator population causesselection for lower emigration rates of the herbivores (i.e., an increased tendencyto stay in the herbivore aggregation), whereas a prevalence of killers causes selec-tion for higher herbivore emigration rates. The ES emigration rate m∗

N appears tobe always intermediate between 0 and rN . Thus, herbivores may still aggregate inthe face of killer-like predators.

Much remains to be learned as to how the evolution of plant defense strate-gies interferes with that of herbivore emigration. Increased efforts in direct plantdefense probably decrease the per capita rate of herbivore population growth rN ,and as a by-product this triggers selection for a higher ES emigration rate of theherbivores m∗

N . Thus, ultimately the effective per capita rate of herbivore popula-tion growth, rN − m∗

N , decreases even more. This paves the way for the evolutionof feeding deterrents. The same applies to increased investments in indirect plantdefenses. When plants promote the per capita predation rate k or the per capita


0.60.5 0.7 0.8 0.9 1.0Prey growth rate, rN

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Figure 22.8 ES patch-emigration rates of prey in a predator–prey metapopulation. (a) TheES prey emigration rate m∗

N as a function of predator growth rate rP . (b) Relation betweenES emigration rate m∗

N and the prey growth rate rN . (c) Relation between ES emigrationrate m∗

N and the prey consumption rate k. Default parameter values: Nres(0) = 49 (a)or 99 (b, c), Nmut(0) = 1, P(0) = 1, rN = 1, rP = 1.5, k = 1. Source: Egas et al.(unpublished).

rate of predator population growth rP , the by-product is that selection favors in-creased ES emigration rates of the herbivores, thereby lowering the effective rateof herbivore population growth, rN − m∗

N . Thus, plants may also invest in re-leasing herbivore deterrents, signaling a high risk of being eaten by predators, andthe herbivores are selected for vigilance in detecting the actual presence of preda-tors. There are several examples of herbivorous arthropods that prefer plants witha lower risk of falling victim to natural enemies, despite their lower food quality(Fox and Eisenbach 1992; Ohsaki and Sato 1994). However, it is still unclear whythe low quality plants are visited less frequently by the natural enemies of the her-bivores. Another speculative, but potentially nice, illustration of plants signalingtheir predator-defended state to herbivores is found in the work of Bernasconi et al.(1998). When corn leaf aphids feed upon them, maize plants respond by releas-ing a blend of volatile compounds that repels other corn leaf aphids in search forhosts and also attracts parasitoids and lacewings. Interestingly, the blend of plantvolatiles contains a monoterpene, (E)-β-farnesene, that corresponds to the alarm


signal released by the corn leaf aphid upon predator attack. Another potential ex-ample of plants signaling predation risk is given by Pallini et al. (1997), who foundthat spider mites prefer odor from spider-mite infested cucumber plants over odorfrom thrip-infested cucumber plants, whereas the thrips show no preference. Bothspider mites and thrips are herbivores, but the thrips can also act as a predator ofspider-mite eggs. Thus, the olfactory avoidance-response of the spider mites maybe to avoid competition as well as predation risk. Recently, Pallini et al. (1999)found more evidence for the avoidance of predation risk in spider mites. Theydemonstrated that spider mites prefer odor from plants with spider mites aloneover odor from plants with spider mites and the predatory mite P. persimilis. Pos-sibly, the odor signal comes from conspecific spider mites that had direct contactwith the predators, but this remains to be shown.

The plant’s dilemma: direct, indirect, or no defense?By investing in direct and indirect defenses, a plant gains protection against her-bivory, but in doing so it also benefits its neighbors. If these are close kin, anindividual plant also increases its inclusive fitness by investment in defense; but ifnot, it may well promote the fitness of its competitors for the same space and nutri-ent sources. Thus, the neighbor gains associational protection (Atsatt and O’Dowd1976; Hay 1986; Pfister and Hay 1988; Fritz and Nobel 1990; Fritz 1995; Hjälténand Price 1997). This leads to the plant’s dilemma: should it defend itself, therebybenefiting its neighbors as well, or decrease its defensive efforts? The solution issimple: the defenses should protect the plant without benefiting palatable neigh-bors too much. When its neighbors are well defended, a plant can afford to investless itself.

When plants are (constrained to be) either undefended or well defended andherbivores do not discriminate between them, three outcomes are possible:

� All plants are palatable;� All plants are well defended;� There is a stable mixture of palatable and well-defended plants.

Coexistence of the two types is possible when either of them increases when rare;in a population of well-defended plants a rare palatable plant can easily gain cheapprotection by associating closely with a well-defended plant, whereas in a popula-tion of palatable plants a rare, well-defended plant does better as it benefits onlyfew of the palatable individuals and, hence, increases the average fitness of thepalatable plants only very little. When either of the two types gradually increasesits share in the total population, the benefits wane and ultimately balance the costs,thereby giving rise to a polymorphic plant population (Sabelis and de Jong 1988;Augner et al. 1991; Tuomi and Augner 1993; Augner 1994).

The conditions for polymorphism are quite broad, but some of the critical as-sumptions are not generally valid. For example, herbivores are likely to distinguishbetween palatable and well-defended plants. In that case, an individual plant islikely to benefit from direct defenses and may even drive the selective herbivores


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Figure 22.9 The effect of herbivore mobility (horizontal axis) on the parameter areas inwhich the ESS is to kill the herbivore (dark gray region), to kill part of the herbivores(intermediate, white region), and not to invest in killing herbivores at all (light gray region).The extent of these areas depends on the ratio of marginal costs of plant defense and theinitial risk of herbivory. The cost of herbivory equals one if the herbivore survives, and 0.5if it dies. Source: Tuomi et al. (1994).

toward the palatable plants. It should be noted that this mechanism does not applyto indirect defenses. Predatory arthropods are usually more mobile than the prey(stages) they attack and they readily move from the plant that employs them asbodyguards to a neighbor plant when the latter is under herbivore attack. Thus,even when the herbivore is a selective feeder, palatable plants profit more easily bysettling close to a plant defended by predatory arthropods as bodyguards. Clearly,this mechanism promotes polymorphism (Sabelis and de Jong 1988). However,when defensive plant strategies are not discrete, but continuous (i.e., they coverthe full range of possible investment levels), then there may be no polymorphismbecause ultimately all the plants will exhibit the best average defensive response.

The latter case was analyzed by Tuomi et al. (1994). They assumed that thecost of defense increases linearly with the probability of killing the herbivore, theslope being referred to as the marginal cost of defense (i.e., how fast costs increasewith the impact of defense on the herbivore). The ES lethality level depends onthe risk of herbivory, the marginal cost of defense, and the mobility of the her-bivores between neighbor plants, as shown in Figure 22.9. When herbivory risksare low and marginal costs of defense high, then it does not pay to kill the herbi-vore. However, when the risk of herbivore damage is high and marginal defensecosts are sufficiently low, then it pays to kill the herbivore. For intermediate ra-tios of marginal defense costs and risk of herbivory, ES lethality depends on themobility of the herbivore between neighboring plants (Tuomi et al. 1994). Obvi-ously, high mobility causes neighboring plants to share the same herbivores andselects for lower lethality levels, whereas low mobility selects for increased lethal-ity. It is becoming increasingly clear that neighboring plants may communicate viadamage-related signals (Farmer and Ryan 1990; Bruin et al. 1992, 1995; Shonleand Bergelson 1995; Adviushko et al. 1997; Shulaev et al. 1997), so it may well


be that plant defenses include strategies conditional upon the neighbor’s state, asdefined by:

� Whether it is actually under attack;� Its defensive response.

This is a largely open problem in need of further theoretical and experimentalwork.

Whether the effects of defensive efforts occur in discrete jumps or are moregradual is an important determinant of the existence of polymorphism, but themost relevant message is that in both cases associational protection may lead to alower average investment in defenses. This applies to direct defenses (Tuomi et al.1994), as well as to indirect defenses (Sabelis and de Jong 1988).

But coevolution may act as a boomerang . . .

The most elusive unknown of all is the interplay between metapopulation dynam-ics and evolution at all three trophic levels. To assume a steady state metapopula-tion is clearly an oversimplification in view of the complex dynamics (e.g., bista-bility, chaos) that may arise by adding an extra trophic level to ditrophic models(Sabelis et al. 1991; Jansen and Sabelis 1992, 1995; Klebanoff and Hastings 1994;Jansen 1995; Kuznetsov and Rinaldi 1996) or the complexities that may arise fromthe interactions within food webs of arthropods on plants (intraguild predation;“prey-eats-predator”; apparent competition; Holt 1977; Polis et al. 1989; Polisand Holt 1992; Holt and Polis 1997). Thus, where the tritrophic system will settleevolutionarily is very hard to predict.

To illustrate this, it is worthwhile to carry out an – admittedly speculative –thought experiment. Consider what will happen when plants evolve to invest morein direct and indirect defenses, and predators are initially of the killer type. Firstand foremost, increased defensive efforts by the plant decrease the size of the her-bivore’s metapopulation. Subsequently, the size of the predator’s metapopulationdecreases which in turn causes a drop in the rate of predator invasion into herbivorepatches. As a consequence, the probability of coinvasion of predators with differ-ent prey-exploitation strategies into the same herbivore patch decreases, therebyproviding a selective advantage to predators that are more milker-like. In addition,increased plant defense promotes herbivore emigration and decreases the size oflocal herbivore populations. This also decreases the probability of predator coin-vasion and thus selects for milkers. Thus, the plant’s investment in defense mayultimately result in ineffective predators; this we call boomerang coevolution. It istypically the consequence of adding one more trophic level to an exploiter–victimsystem and allowing strategies of exploitation and defense to vary at each trophiclevel.

A similar thought experiment can be carried out for the case that not only doesthe plant benefit from its own investment in direct and indirect defenses, but so doits neighbors, who may well be competitors (Sabelis and de Jong 1988; Augneret al. 1991; Tuomi et al. 1994). Again, increased investment in plant defense


causes a boomerang effect because neighboring plants profit and allocate the en-ergy saved directly to increase their seed output or indirectly by increasing theircompetitive ability.

Boomerang coevolution arises through the impact of plant defenses on alter-native allocation strategies of neighboring plants and via the positive effect onthe milker-like prey-exploitation strategies. This may well be the evolutionaryreason why many plant species channel so little of their energy resources intodefense against herbivores (e.g., “cheap” carbon-demanding defenses rather than“expensive” nitrogen-demanding defenses), whether this be direct defense (Simmsand Rausher 1987, 1989; Herms and Mattson 1992; Simms 1992) or indirect de-fense (Beattie 1985, p. 52; Dicke and Sabelis 1989). Hence, we hypothesize thatboomerang coevolution constrains the plant’s investment in direct and indirect de-fenses. Low investment, however, does not necessarily imply that plant defenseshave a low impact. This entirely depends on the quantitative details of how theoffensive and defensive traits of the interacting organisms at all three trophic lev-els settle evolutionarily. In other words, the impact of the plant’s defenses in-creases if herbivores become more milker-like and predators more killer-like, andthe impact decreases when herbivores become more killer-like and predators moremilker-like.

22.5 DiscussionIn this chapter we give a game theoretical view of the evolution of exploitation anddefense strategies in tritrophic systems. Do we now understand why plants investin promoting the effectiveness of the herbivore’s enemies and can we learn fromthese insights to manipulate the virulence of the herbivore to the plant and that ofthe predator to the herbivore?

Are tritrophic systems prone to evolve conspiracy?It is commonly believed that plant–predator mutualisms readily evolve because it isin the interests of both the plant and the predator to act against the herbivores (Priceet al. 1980). Indeed, much evidence shows that plants can provide alternative food,shelter, and SOS signals utilized by the natural enemies of the herbivores, but whatis still lacking is a critical assessment of the overall benefits to the plant. Muchwork is required to detect the role of cheating. Clearly, the plant cannot controlwho is benefiting from the facilities offered by the plant. Alternative food, shelter,and SOS signals are all open to “misuse” by the plant’s enemies or inefficient nat-ural enemies of the herbivores (Sabelis et al. 1999a, 1999b). In addition, there isa need to analyze how investments in plant defense influence competition amongneighboring plants, since one plant may profit from the bodyguards retained andattracted by the other. Again, the investor cannot monopolize the benefits that ac-crue from bodyguards, since they move to wherever their victims are. Finally, thebenefits to the plant depend on the number of predators in the surrounding envi-ronment and these numbers fluctuate. Costs and benefits of indirect plant defenseare therefore expected to vary greatly in time and space (Bronstein 1994a, 1994b).


Thus, even though plenty of evidence shows that plants invest in attracting, retain-ing, feeding, and protecting bodyguards and that the bodyguards can make gooduse of the facilities offered by the plant, it is not an easy task to demonstrate in thefield that predators assume the role of the plant’s immune system.

Whereas a net benefit of indirect plant defenses is still to be shown experimen-tally, the rationale that underlies the evolution of indirect defenses is not fullyestablished either. In this chapter we analyze the interaction between a plant,its neighbors, its herbivores, and the herbivore’s enemies as a game of defense(among neighboring plants), escape (among herbivores), and resource exploitation(among herbivores and among predators). We explain that the mobilities of theherbivore and its predator play a crucial role in determining the extent to which aplant can reap the benefits from investing in direct or indirect defense (Tuomi et al.1994). In addition, we discuss how prevailing resource exploitation strategies maychange through metapopulation structure dynamics and migration via their impacton the probability of coinvasion of exploiters with different strategies of exploit-ing the resource. We argue that there is an interplay between plant defense, plantcompetition, exploitation of host plant, and prey in tritrophic systems. We alsospeculate that there is room for unstable evolutionary dynamics (e.g., boomerangcoevolution), which may give way to selection for low investment in plant defenseand milker-like predators. Indeed, empirical observations indicate that indirectdefenses are not very costly, but killer-like, not milker-like predators seem to pre-vail in the field. This contrast between prediction and observation may indicatethat predators have no control over the exploitation of their resources. This mayarise from external causes, such as mortality through abiotic factors (wind, rain,fire) and competition with other natural enemies (pathogens, parasites, predators).To specify the conditions under which low-cost indirect defenses and killer-likepredators evolve, our game-theoretical analysis needs extension to include evo-lution in the full tritrophic system and its interaction with ecological dynamics.This approach may lead to a more sound rationale for the “world is green” hy-pothesis. The commonly accepted hypothesis that mutualism readily evolves inplant–herbivore–predator systems because “it is both in the interest of plants to getrid of the herbivores and in the interest of the predators to find herbivores as prey”is as yet unfounded.

Perspectives for virulence managementGiven that the theory on evolution and defense in tritrophic systems is rather imma-ture, it is too early to consider direct applications, but there are several potentiallyimportant implications for virulence management. First, we may ask how twostrategies, biological control and breeding for plant resistance, to combat plantpests influence ultimate success in crop protection. One-sided measures to in-crease direct plant defense may ultimately select for mild predators and, therefore,increased herbivory may be the end result. It seems wise to also breed for increasedindirect defenses, because this promotes multiple colonization by predators, whichwill in turn select for increased predator virulence. Second, an old debate among


biocontrol workers is whether to release single or multiple species of predators.The latter seems best on the condition that it promotes local competition betweenpredators, because this will increase their virulence. Third, we may wonder howmass rearing influences the virulence of predators before their release in the field.We suspect that mass rearings are like an undepletable prey patch and that leav-ing that patch is unlikely to promote within-rearing success. Hence, there will beselection for predators that suppress their tendency to disperse as long as there isfood. This inadvertent selection for killer-like predators is good news for biolog-ical control workers aiming at fast suppression of the plant pest near the site ofpredator release, but are the aims of biological control over large areas served inthis way, because at that spatial scale dispersal may become a vital trait of a suc-cessful biocontrol agent. Moreover, predators less efficient in clearing pest arthro-pods from a plant (milkers) may produce more dispersers and therefore promotetheir chances to reach distant sites. Clearly, there is every reason to reconsidercarefully the criteria for a good biocontrol agent when the aim is to achieve con-trol over a large spatial scale. Fourth, there is the long-standing question of wherebest to collect candidates for biological control. We expect to find milker-typepredators near the borders of the geographical range (where predator densities arelow) and killer-type predators in the center (where predator densities are high; seePels and Sabelis 1999), but much more (theoretical and empirical) work is neededto substantiate this claim. A more elaborate discussion of these four implicationsis given in Chapter 32, albeit based on predictions of how selection molds predatorvirulence only and not on how it acts on virulence and defense in systems withthree trophic levels.

Appendix 22.A Evolutionarily Stable Herbivore Emigration RateAssume a metapopulation of patches with local interactions and global migration. As in VanBaalen and Sabelis (1995c), all the patches start with exactly the same number of predatorsand prey (metapopulation-wide equilibrium and no stochastic variation in the number ofcolonizers), that is, N0 = N (0) and P0 = P(0), and the redistribution of predators andprey occurs after completion of the local interaction (sequential interaction rounds). Toassess the evolutionarily stable emigration rate (given rN , k, and rP ), a measure of preyfitness is defined as the total number of herbivore emigrants per herbivore foundress, w =m N (Ntot/N0), where Ntot is the total number of prey produced in a patch. Defined in thisway, the fitness measure reaches an optimum between no migration (m N = 0; extinctionof all patches) and an emigration rate equal to the per capita growth rate (m N = rN ; nooffspring produced in the patch).

Further, assume that the two types of herbivore clones are attacked in proportion to theirrelative abundance, but that the mutant is so rare that Nres + Nmut ≈ Nres. Then theherbivore dynamics in the patch are entirely dependent on the resident population and therare mutant’s presence does not influence the growth of the resident herbivore population.As a result of this last assumption the model yields an analytical solution for the fitness ofthe rare mutant. The dynamics of the rare mutant are given by


d Nmut

dt= (rN − m N ,mut

)Nmut − k P

Nmut

Nres. (22.7c)

Solving Equations (22.7a), (22.7b), and (22.7c) gives an explicit description of how thenumber of mutant herbivores changes with time,

Nmut(t) = N0,mut

N0

{N0e(rN −m N ,mut)t − P0

k

rP − (rN − m N ,res)

[e(rP+m N ,res−m N ,mut)t − e(rN −m N ,mut)t

]}, (22.7d)

with N0,mut = Nmut(0).The fitness of the rare mutant wm is the sum of dispersing mutants divided by N0,mut,

wm = m N ,mut

∫Nmut (t)

N0,mut, (22.8a)

or

wm =m N ,mut

N0

{N0

e(rN −m N ,mut)τ − 1

rN − m N ,mut− P0

k

rP − (rN − m N ,res)

[e(rP+m N ,res−m N ,mut)τ − 1

rP + m N ,res − m N ,mut− e(rN −m N ,mut)τ − 1

rN − m N ,mut

]}. (22.8b)

The evolutionarily stable emigration rate m∗N can be found as the emigration rate of the

resident population for which no mutant with a different emigration rate has higher fitness,

dwm

dm N ,mut

∣∣∣∣m N ,mut=m N ,res

= 0 , (22.9)

Equations (22.8b) and (22.9) yield an implicit function, from which a solution for m∗N can

be obtained,

m∗N =

(N0 + k P0

rP−�

) (e�τ −1

�

)−(

k P0rP −�

) (erP τ −1

rP

)(

k P0rP−�

)(erP τ −1

r2P

− τerP τ

rP

)−(

N0 + k P0rP−�

) (e�τ −1

�2 − τe�τ

�

) ,

(22.10a)

where � = rN − m∗N and τ is the total time of the predator–prey interaction,

τ = 1

rP − �ln

(1 + rP − �

k

N0

P0

). (22.10b)

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c International Institute for Applied Systems Analysis 22€¦ · Sabelis MW, van Baalen M, Pels B, Egas M & Janssen A (2002). Evolution of Exploitation and Defense in Tritrophic